% 
% For illustrative purposes this duplicates the MATLAB results on 
% epage 117 from the book.
% 
% Written by:
% -- 
% John L. Weatherwax                2008-11-24
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

addpath( '../../AdaptiveFilteringCode/' ); 

clear functions; 
clear; 
%clc; 
close all; drawnow; 

randn('seed',0); rand('seed',0); 

N  = 2^10;
n  = 0:(N-1); 

plt_inds = 512:(2^(10));

% the random driving input noise ... used in creating the observed noises v_1(n) and v_2(n) 
% 
v  = randn(1,N);                              

% our input signal is given by x(n) ... 
% ... we want to predict this signal from the previous two values:
% 
a_coefs = [ 1, -0.601, +0.7725, ];
b_coefs = [ 1 ]; 
x = filter( b_coefs, a_coefs, v ); 

% plot the input signal x(n)
% 
fo=figure; hd=plot( n(plt_inds), x(plt_inds), '-og', 'markersize', 6 ); hold on;    % <- the observed signal ...

M = 2; 

% 
% for one learning rate: 
% 
mu = 0.02; 
[w,y,e,J,w1] = aalmsonesteppredictor(x,mu,M); 

figure(fo); plot( n(plt_inds), y(plt_inds), '-xr' ); % <- the predicted signal 

fe = figure; eh1 = plot( n, e, '-k' ); hold on; % <- the error as a function of n 

fw = figure; ws1 = plot( w1, '-' ); hold on; % <- the convergence of the weights ... 

% 
% for another learning rate: 
% 
mu = 0.005; 
[w,y,e,J,w1] = aalmsonesteppredictor(x,mu,M); 

figure(fo); plot( n(plt_inds), y(plt_inds), '-xk' ); axis tight; 
xlabel( 'n' ); ylabel( 'predictions' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter7/lin_pred_signal_plus_pred.eps', 'epsc' ); 

figure(fe); eh2 = plot( n, e, '-r' ); axis tight; 
xlabel( 'n' ); ylabel( 'prediction error' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter7/lin_pred_error.eps', 'epsc' ); 

figure(fw); ws2 = plot( (w1), '-' ); axis tight; 
plot( n, -a_coefs(2)*ones(1,N), '-g', 'LineWidth', 4 ); 
plot( n, -a_coefs(3)*ones(1,N), '-g', 'LineWidth', 4 ); 
%ledgend( [ ws1, ws2 ], {'','','',''} ); 
xlabel( 'n' ); ylabel( 'weight convergence' ); 
title( 'convergence of the weights' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter7/lin_pred_weight_conv.eps', 'epsc' );